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Abstract
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On asymptotically complex hyperbolic (ACH) Einstein manifolds, we consider a
certain variational problem for almost complex structures compatible
with the metric, for which the linearized Euler–Lagrange equation at
Kähler–Einstein structures is given by the Dolbeault Laplacian acting on
-forms
with values in the holomorphic tangent bundle. A deformation result of Einstein
ACH metrics associated with critical almost complex structures for this
variational problem is given. It is also shown that the asymptotic expansion of a
critical almost complex structure is determined by the induced (possibly
nonintegrable) CR structure on the boundary at infinity up to a certain
order.
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Keywords
asymptotically complex hyperbolic spaces, almost CR
structures
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Mathematical Subject Classification
Primary: 53C15
Secondary: 32T15, 32V15, 53B35, 53C25
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Milestones
Received: 14 April 2020
Revised: 6 May 2021
Accepted: 24 July 2021
Published: 10 November 2021
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